FTCE Professional Education Practice Exam

Which statement is correct about rectangles and trapezoids?

1. Some rectangles are trapezoids

2. All rectangles are trapezoids

3. Some rectangles are parallelograms

4. No rectangles are trapezoids

The correct answer is: No rectangles are trapezoids

The assertion that no rectangles are trapezoids is incorrect because a rectangle is actually a specific type of trapezoid. A trapezoid (or trapezium) is defined as a quadrilateral with at least one pair of parallel sides. Since a rectangle has two pairs of parallel sides, it qualifies as a trapezoid as it meets the minimum requirement. In the correct context, the first option indicates that some rectangles are indeed trapezoids. It notes that rectangles fit the broader definition of trapezoids because they also possess parallel sides. Understanding the properties of these shapes is key. Rectangles are a subset of quadrilaterals with opposite sides that are equal and all angles measuring 90 degrees. Trapezoids, on the other hand, are characterized by at least one pair of parallel sides, and rectangles fall comfortably within this category. Recognizing the relationships between these geometric figures helps clarify how they are categorized within the broader study of geometry.